各類梁的彎矩剪力計算匯總表

1、表1簡單載荷下基本梁的剪力圖與彎矩圖梁的簡圖aIlF否息剪力Fs圖彎矩M圖2一、qqa(21-a)8122、qa(1-a)a(21二a)2111-3a-|M表2各種載荷下剪力圖與彎矩圖的特征某一段梁上的外力情況剪力圖的特征彎矩圖的特征無載荷11水平直線斜直線或集中力1FFL突變-F轉(zhuǎn)折,集中力偶Me-無變化突變/Me均布載荷口qn斜直線拋物線L或零點極值表3各種約束類型對應(yīng)的邊界條件約束類型位移邊界條件力邊界條件（約束端無集中載荷）固定端w=0，6=0一間支端幺尸w=0M=0自由端11一M=0，F(xiàn)S=0注：力邊界條件即剪力圖、彎矩圖在該約束處的特征。序號常用截面幾何與力學(xué)特征表表2-5截面邊緣

2、至.主軸的距離y對主軸的慣性矩11,y=TA2t=Th_i.(bj+2b)h*尸3(如+b)(b+2h"以=3+，)(乂+4加+")/336(6+bj截面抵抗也W回轉(zhuǎn)半徑11卬=而Dt=0.289ftW尸古妒W古而i=0.236h(M+4砧e+“)MWl2(b2b3+4助+bf)ML12(261+fr),Q.23獨/,i.Akk4,2-b+bi5+4M#加注：1.I稱為截面對主軸（形心軸）的截面慣性矩（mm4）?；居嬎愎饺缦拢篒=y2dAAI2. W稱為截面抵抗矩（mm3）,它表不截面抵抗彎曲變形能力的大小，基本計算公式如下：W=ymax3. i稱截面回轉(zhuǎn)半徑（mm）,

3、其基本計算公式如下：i=4,上列各式中，A為截面面積（mm2）,y為截面邊緣到主軸（形心軸）的距離（mm）,I為對主軸（形心軸）的慣性矩。5.上列各項幾何及力學(xué)特征，主要用于驗算構(gòu)件截面的承載力和剛度。2.單跨梁的內(nèi)力及變形表（表2-6表2-10）（1）簡支梁的反力、剪力、彎矩、撓度表2-6序次圖類圖示項目計算式1荷載尸TJ反力J?A=Rh=剪力y網(wǎng)vs=-零短彎矩Ma=-Ef.剪力撓度_Fl3w-48£ihnwn2荷載月Jc反力Ra="F*=十F剪力F產(chǎn)Rr*Yr=-RbL上】彎矩一Fta>j-彎矩?fù)隙热簟Ｐr，在上當(dāng)J七（fl+SfT期力Mi山L_Ffr1(a22

4、ab)3w-9EkV33荷載上反力Ra=Rr=F="Zi1P一：剪力人；vB=-j?b彎矩穹矩Maj=Fa.：'Z的力nn.一，HillI撓度Wmoi=24El荷載LteJ3或反力Ra=b二年F剪力Fa=R小VB=-fi0TT*'-B1彎矩pr彎矩Ma=fFL剪力撓度19F-皿必一3B4E1血皿Lil5荷載反力R&=R®="醒ALLiLl.LTITLJr剪方Va=R*;Vb=-彎矩彎拒M*=/以，剪力撓度5金*a384E.序次圖類圖示項目it算式1荷載Xh反力剪力VB-/?B彎矩rrrrrnrrrfTnTI彎矩Ml-FkIMa=Mr=-F&

5、#163;穹矩_<rnTiiirnTi彎矩M*=-F(工rh工M,=-Fb剪力-nnmnnm撓度w*-6EII3i)序次圖類圖示項目計算式1荷載4:反力比a="eRb="f1：2剪力Va=Ka；vb=-j?b彎矩I一rfp彎矩璉;MB=-Fl“io剪力in山hi11I1JL1111撓度當(dāng)工=0,447七時，Hg=0,Cl0932a上I2荷載jst4P反力R祟；3都-£)剪力3Ra；*自彎矩彎矩當(dāng)工=以時，3-y-j剪力_撓度CH段；ua-Ra（3f。一工）一3FfcO+Fa）310總JIhllIIIJa3荷載AirLLpb反力RL（2-3寧+3Rl/（2+3

6、予-3/）：口一2"四力"E公Vb=-Rr彎矩7皿1山爐加彎矩Mc=Ra；-竽1-?。┘袅撓度CD®；wK=Zr<7（jRa3產(chǎn)工工，）=3F（Z2"2al+2a.2）wCij&J+F（x-a）3II1!N1口ALILmi彎短時如FTTTW翦力nnnnni1bBS.荷載2彎矩tthizlfll剪力THjjT：lll1lllll項目計算式反力Ra=Re=/f剪力A-Ra3%=-Rb彎矩Mg=十9撓度Tt)=192EI反力w臂。沖竽)剪力=¥b=-Hr彎矩iw2Ed產(chǎn),M皿二Me.3-t撓度±l_2aZ_u_t_2F若工乩

7、當(dāng)±-3a+b此M"一羽a(3.+6*序次圖類圖示項目計算式1荷裁ra反力心二八+十年,口馬-一節(jié)C/。/剪力Vc=-F;5-Rr-FA彎矩>fnTTnnmTT彎矩Mx=Ma=-Fa剪力(mi'ttu；撓度加廣普(1+亍)當(dāng)工=&+Q+5£時，卬面=-0.0642嘴£1川III2荷載LJ反力J?A工RB=F<T剪力¥尺=-Ra：/=Rb彎矩/ffUWIHHIIRK彎矩M產(chǎn)iVfB=-Fa剪力EBjmu撓度寓Ri亍當(dāng)工=&+0.5!時，w貓尸一黑OjDI3 .等截面連續(xù)梁的內(nèi)力及變形表（1）等跨連續(xù)梁的彎矩、剪

8、力及撓度系數(shù)表（表2-11表2-14）1）二跨等跨梁的內(nèi)力和撓度系數(shù)表2-11序次荷載圖鹿內(nèi)最大彎矩支座彎短«力跨度中點撓度MiMiMbVAV酸1vcW1W2140.0700,070-0.1250.375-Q.6250.625-0,3750.5210,521匚：11,11111'11.11月4一L一j(A/i)(AA)2Allui'Ct0.096-0.0630.437-0.S630.063仇0630,912-03913A-+4八，Rr0.1560*1560.1880.312-0.6880.688-0,3120.9110.9114rTFBC0.203-0.094Q.4Q

9、6-0.5940.0940.0941.497-0+5864注：1.在均布荷載作用下：”=表中系數(shù)xql2；丫=表中系數(shù)xql；亞=表中系數(shù)父ql。100EIFl32.在集中荷載作用下：”=表中系數(shù)XFl;丫=表中系數(shù)XF;亞=表中系數(shù)父。100EI例1已知二跨等跨梁l=5m,均布荷載q=11.76kN/m,每跨各有一集中荷載F=29.4kN,求中間支座的最大彎矩和剪力。解1支=(-0.125X11.76X52)+(0.188X29.4X5)=(36.75)+(-27.64)=-64.39kN-mVb左=(-0.625X11.76X5)+(0.688X29.4)=(36.75)+(20.23)=

10、-56.98kN例2已知三跨等跨梁l=6m,均布荷載q=11.76kN/m,求邊跨最大跨中彎矩。解M1=0.080X11.76X62=33.87kNm。2)三跨等跨梁的內(nèi)力和撓度系數(shù)表2-12序次荷載圖跨內(nèi)最大等矩支座彎矩翦力跨度中點梯度M1M2MbMeVA丫3vD的1W21O.OBOO+O25-0,100-0.1000+400-0.6000.500-0.500Q.600-0,4000.6770.0520.677knrirtnnirmnirj注：1.在均布荷載作用下：”=表中系數(shù)xql2；丫=表中系數(shù)xql；亞=表中系數(shù)父ql4100EI2.在集中荷載作用下：”=表中系數(shù)XFl;丫=表中系數(shù)X

11、F;亞=表中系數(shù)父一亡，100EI3）四跨等跨連續(xù)梁內(nèi)力和撓度系數(shù)表2-13注：同三跨等跨連續(xù)梁。4）五跨等跨連續(xù)梁內(nèi)力和撓度系數(shù)表2-14荷載荷圖彎矩黃力跨度中點撓度M中Ma中M,中A!聯(lián)Me支VA曠色卜斷%皿加3口.046-0.105-0.0790.3940.6060.526-0,4740,5000.6443.1510,315川口"|"4c%上苫”*由，*Q，0.1710.112hl嬰-0.158-0.1180.342-0.6580.540-0.4600.5001.097口.356U.6(B1AC小口FJX此門仁門:0.240口.10。隊122-0.281().2110

12、.713-1.2011.071-0.9301.0001.795).479).918q產(chǎn)1,，"%/南F4I（2）不等跨連續(xù)梁的內(nèi)力系數(shù)（表2-15、表2-16）1）二不等跨梁的內(nèi)力系數(shù)表2-15XX荷載4-i-，iI_q_女也JnilAB1J'產(chǎn)打AjA<w_u_>>“如(MQMfiAVa爐儂(.Va)F防（憶）VcMab3血)vA（噎）Mbc(M皿)Vc(VJ1.0-y.iisu0.07030,07030.3750-0.62500.6250-0*37r500.09570.43750.0957-0.4375L1-0.13880.06530.08980.361

13、3-0,63870.6761-0.42390.D97D0.44050.1142'0,47fi0L2TL155。U.Q595ILins0.3450-0.6550(L7292-0.47080.09620,44320.1343-0.51821,3-0.17380.05320.13330.3263-0.673707836-0.51640,09930.44570.1558-0.55821.4-0.195。O,G4650.1572U.3O50-0.69500.8393-0.5607UJ0030.44790.17880.59791.5-0.21880.03960.18250.2813.*0,7187

14、08958-0.6G420.10130,45W)0.2032-0.63751.60,24500.0325Q.2Q920.2550-0.74500.95310.64690.1021依45190.2291-0.6769】.7ft.27330.0256k2rM0.2263-0.7737L0L10-0.6弱00.10290,45370.2564-0.71621.8-0.305Q001900.26690.19500.8050L0694-0.73060.10370.45540.2850-0.75541*9-0,3388口,01300.29780.16130.83871.1283-0,7717fl.1044

15、0.45690.3155-0.79442.00.37500.007S0,330L0.1250-0,37501.1875-0.81250.10500,45830.3472-0.83332.25-0.47660.00030.417P0,02340.9766L336g-0.91320.106504615Q.4327-0.93032.5-0.5938負(fù)值0.5126-0.09381.09381.48751l4】250.1078(M6430.5272-1.0266注：1.”=表中系數(shù)xql21；丫=表中系數(shù)xql1；2.（Mmax）、（Vmax）表示它為相應(yīng)跨內(nèi)的最大內(nèi)力。2）三不等跨梁內(nèi)力系數(shù)表2-1

16、6載、irmigUJIII1141X.g_IllIrHl11uL741-*-411!1h1111liiinh=nlCZ!,.bt、含L4-ffAJLUAA1zEA|!1.九lhLh=nhi、數(shù)-JJ*“TT上彳LM1s.1M嵋M/VaVbSL喂Mb(Mz)Vb左（嚏）(k)Mab(JW(VaMbc(Mm)（M-O.OS31口.0869一0.06310.4169-0.58310.2000-0.09()2-0.5962O.46OS0,08900.42L90.01500.5=仇網(wǎng)40.08別J-0.0491"41960,58040.2500-0.0947-59470.45020A>9

17、1)30.42860,02230,6-0,08000.0882-0.03500.4200-0,58000.3000-0.0952一0.59520,46030.09430.43420,03080.7-0.08190,0874-0.02060.4181-0*58190.350。-O09R-0.59790.482596,I0.43000.04050.80.08590,0857-0.00590.4141-0.5浮590.4000-0.1021-0.602J0.5116(LI19&J0.4432!0.05090.9-0.09130.08330,00950.4082-0.591N0,4500-0.

18、1083-0.60830.54%0.09980.44680.0625L0-0.10000.08000.02500,40000.600。0.5000-0.1167-0.61670.58330.1013(L4SU00.07501.1-O.UOO0.07610.1)4130.390。-0.61000.5500-0.12670.62670.62330.10250.45280.08851.2-D.121B0.07150.05820,3782-0,62180.6000-0.1385-0.63850.66510.103。r0.45540.10291.3-0.13550.(16640.07580.3645-0

19、.63550.6500-0.1522-0.6522W.70B20.104-70.45760.11S21,4-0.15100.060。0.09400.3490-0.65100.7000-U.1676-0,6671&0.75250.10570.45970.13441.5-O.16S30.05500.11300.3317-0.66830.75典0.1848-0.6S4810.79760,10650.46150,15141.6-038740.04890.13270.3127-Ux6R730.8000-IL2037-0,70370.H4340,1or0,46320.16941,7-0.20820

20、.04260.15310,29180.70820.S50C-0.2244-0.72440.88970.10800.46480.18B31.8-0.2304C0.03626.17420.2692-&.73080.9000-O.246S-0.746B0.9366仇1U870.46620.20801,9-0,25520,03000.19610,2448-0.75520.9500-0.2710-0.77100.08460.10930.46750.22862,0-0,28130.(12390.21880.2188-0*78121.0000-0,2969796!1.03120.1。則0.46880

21、.25002,25-O,S54O0.01060.27股0.14620-35381.1250-0.3691-0.86911.15110.11110,47140.30742.5-0.43750.001903437-0.06250.93751.2500-0.45210.95211,27220.11220.47370.3701注：1.”=表中系數(shù)xql2i；丫=表中系數(shù)xqli；2.（Mmax）、（Vmax）為荷載在最不利布置時的最大內(nèi)力。4.雙向板在均布荷載作用下的內(nèi)力及變形系數(shù)表(表2-17Y2-22)符號說明如下：剛度K二Eh212(1-2)式中E彈性模量；h板厚；V泊松比；、max分別為板中心

22、點的撓度和最大撓度；Mx為平行于lx方向板中心點的彎矩；My為平行于ly方向板中心點的彎矩；Mx0固定邊中點沿lx方向的彎矩；My°固定邊中點沿ly方向的彎矩。正負(fù)號的規(guī)定：彎矩一一使板的受荷面受壓者為正；撓度變位方向與荷載方向相同者為正。四邊簡支表2-17撓度=表中系數(shù)彎矩之表中系數(shù)式式中1取人和0中之較小者U'%My3MkMy0.500.010130,365(L01740.800,006030.05610.03340.55a.009400.0892口,02100.650,005470.05060.03480.600,008670.08200.02420.900.00496

23、0-04560.03580.650.007960.07500.02710.950,004490.04100.03&40.700,007270.06830.0296LOO0,004060.03680,03680.750.0()6630.06200.0317Uiy筋H叫MX乂方MyM21rmix時工0.500.005040.05830.0060-0.121；0.950J1QJ240.03240.U28。-Q.0S820.550,004920.05630JW81=0.1187。，如0+003680.03281)332-0.09260.600.004720.05390.0104-0.11580

24、.850.001170.0320g03700.09700,650.004480.05130.0126-0.11241|18。0.004730.03260.0424-0/1U140.700.004220,04850.0148-0.10870.750.005360.0319口.0485-0.10560.750.003990.04570.0168-0.104U0.700.006050.03080.0553-0,10960.800.0037610.04280.0187r0.10070.650.006800.02910.0627-0,11330.850.003520.04000.0204-0.096S0

25、.600.007620.0268IL0707-0.11660.90D.003290,03720,0219-0.09220.550.DD8480.02390.0792-D.11930.950.003060.03450.0232-0.08800.500.00935U.02050.1)88。-0.12151.001.000,00285L0.03190,0243-"Q839兩邊簡支，兩邊固定表2-19饒度=表中系數(shù)X*彎矩=表中系數(shù)乂修爐式中，取，和G中之較小者ljlvwMm孫泌筋工W同工MyMi0,500.002610.04160+0017-0+Q843必950.002230.02960.

26、0189-Oh07460,550.002590.04100.0028-O.0S4O0.900.00260kO30A0.0224-0.0797U&0.002550,0如20.0042-0.0834(1.850.003030.03140.0266-0500,650,002500.03920,0057-0.08260.800.003540.03190.03160.09040,700,002430.03790.0072-0.08140.751).004130.03210.0374-0,09590,750.002360.03660-0088-0.07990.700.004820,03180.04

27、41-().10130.800.002280.03510.0103-0.07820.6S0.005600.03080.051fi-0.10660.850.002200.033S0.0118-0.07630.600.006470.02奧00604-0.11140,900,002110.03190.0133-0.07730.550.007430.02670.0698-0/11560.950.002010.03020.0146-0,07210.500.008440,02340.0798-0,11911,001.0。0.001920.02850.0158-0.069g一邊簡支，三邊固定表2-20Uma

28、x疑工My0.500,002580.04080,0028-0.0836-0.05690.55。.002550.039S0.0042-0.0827-0,05700.60k002490.03840.0。59-0.0814-0,05710.650.002400.036S0.0076-0.0796-0.05720.700.。2290.03500.?？?3-0.0774-0.0572U.750.002190.03310.0109-0.0750-0.05720.800.002D80.03100.0124-0.0722-0.05700.850,001960.02890.0138-0,0693-0.05670

29、.900-001840,026B0.0159-0.0663-0,0563D+950.001720.02470.0160-00631-0.0558LOO1.D00,001600.02270.0168-0.0600-0.0550。朋0.001820.02290.0194-0.0629-U.0599U.9Q0,002060.02280.0223-0.06560.06530,850,002330.02250.0255-0.0683-0,07110,800.002620.02190.0290-0.0707-0,07720.750.002940.02080.0329'0.0729-0.08370.700.003270.01940.0370-0.0748-0.09030.650口03650.01750.0412-0.0762-0.09700,600.004030.01530.0454-0,0773-0.10330.550.004370.01270.0496-0.0780-o.nm0.500.004630.00990.0534-0.0784四邊固定表2-21兩邊簡支，兩邊固定表2-22撓度表中系數(shù)父耳ri等矩=表中系數(shù)XqN式中L取和八中之按小者M(jìn),MyM；0.500.004710.05590,0079-0,11790.07860.550.004540